This example illustrates some of the computational difficulties inherent to the algorithms used in this paper. While the explicit forms for the second partial derivatives of the DGA in (REF ), needed to apply [1]}'s algorithm, do exist, the computational burdens may deter most users. A potential solution to this issue is the use of autodifferentiation software to differentiate the DGA. This is an area for further research and development in the field of generalized fiducial inference. Meanwhile, these experiments show that the return projection scheme in [2]}'s (corrected) algorithm is very sensitive to the dimension of the manifold within the ambient space. To explore the sample space where \(A\)  and \(\Lambda \)  are constrained so that \(g^\star (A,\Lambda )=0\) , we perform a simulation study using [2]}'s algorithm only.
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